Why a big suit?

In summary, a German suggested he do something "larger than life" for the theater, and he came up with the idea for the big suit as a theatrical piece for their shows. Byrne's idea was the big suit brought the mundane and bizarre together in a costume.
But I bet you want more, so here we have an interview that gives us the significant and longer reason why?:

Did you invent the Big Suit in Japan?

Yes. I was in Tokyo around 1983. I had just met a fashion designer named Bonnie Lutz. I was smitten with her.

Was she smitten with you? (Lutz is now married to Byrne.)

I think she thought I was bizarre. I was painfully shy. We were having dinner with a German fashion designer.
I told the German that on the next Talking Heads tour, I should have a costume. And the German made a pronouncement,
"'Well David, in the theater everything is bigger than real life.'
I think that was all he said. He didn't say, 'You should have a big suit.' When I had time I would go to a Kabuki theater performance or a noh theater performance or sumo wrestling, just to see all the Japanese stuff. I drew this thing that looked like a Kabuki costume, which is also very rectangular. And the person's head looks like a very small ball. But I thought, What if you take that kind of silhouette, but put it in a Western business suit? I became fascinated with the idea of taking things that look very everyday or commonplace and stretching that in some way, rather than making something totally fantastic and imaginary. I like to restrict myself, OK? It has to look like a suit, even if it's pink fur. It makes reference to the businessman. It has some kind of psychological meaning besides being a costume. He is lost in his suit. Or his suit is swallowing him. It implies all these other things that a wild fantasy costume wouldn't say.

Reference:
From "David Byrne at Ear Inn"
Written by David Bowman
published Oct. 14, 1999, PEOPLE
http://www.salon.com/people/lunch/1999/10/14/byrne